Measuring the Adjusted Monetary Base in An Era of Financial Change

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1 Richard G. Anderson is an assistant vice president and economist at the Federal Reserve Bank of St. Louis. Robert H. Rasche is a professor of economics at Michigan State University and a visiting scholar at the Federal Reserve Bank of St. Louis. We thank Cindy Gleit and Daniel Steiner for excellent research assistance. We also thank the staff of the Division of Monetary Affairs, Board of Governors of the Federal Reserve System, for providing the data used in this article. Measuring the Adjusted Monetary Base in An Era of Financial Change Richard G. Anderson and Robert H. Rasche The adjusted monetary base is an index that measures the effects on a central bank s balance sheet of its open market operations, discount window lending, unsterilized foreign exchange market intervention, and changes in statutory reserve requirements. Such an index is important because the long-run path of a monetary economy s price level is primarily determined by the path of the central bank s balance sheet, adjusted for the effects of changes in statutory reserve requirements. The St. Louis adjusted monetary base equals the sum of the monetary (or source) base and the reserve adjustment magnitude (RAM). This article presents a revised measure of the monetary base and a new RAM. The revised measure of the monetary base differs from previous measures by including all Federal Reserve Bank deposits held by domestic depository institutions; previous measures have excluded the aggregate amount of depository institutions required clearing balance contracts with Federal Reserve Banks. The new RAM recognizes that, since the Monetary Control Act of 90, an increasing proportion of depository institutions have not significantly changed their demand for base money (vault cash and deposits at Federal Reserve Banks) relative to transactions deposits following changes in statutory reserve requirements. revious RAM adjustments have assumed that depository institutions would match changes in their statutory required reserves about dollar-for-dollar with changes in their holdings of base money, following a change in reserve-requirement ratios. The new RAM, constructed from fifteen years of weekly data on more than 0,000 individual depository institutions, measures more precisely the change in the amount of base money demanded by depositories following changes in reserverequirement ratios than did previous RAM adjustments based on aggregate data. THE REVISED MONETARY BASE The measure of the monetary base that was published by the Federal Reserve Bank of St. Louis through September 99 included most, but not all, deposits at Federal Reserve Banks held by domestic depository institutions. The new measure, presented in this article and published by the Bank since October 99, includes all such deposits. The revision increases the level of the base by an amount that varies from zero in 90 up to about $ billion in 99 and 99. Sources and uses of high-powered money for the U.S. economy in December 99 are shown in Table. Most of the high-powered money supplied by the Federal Reserve and the Treasury is represented by currency in circulation and the deposits of domestic financial institutions at Federal Reserve Banks; together, these constitute the monetary base. The old measure of the St. Louis monetary base (line ) equals the sum of currency in circulation outside the Treasury and Federal Reserve (line a) plus the reserve balances of depository institutions (line The concept of high-powered money used in this section is slightly broader than the concept used by Friedman and Schwartz (9). This concept also is widely referred to as the source base; see for example Andersen and Jordan (9). Our usage conforms to the earlier practice of labeling it the monetary base.

2 Table Current and Revised Measures of the Monetary Base, December 99* Factors Supplying Base Money () Reserve Bank credit (a)securities held by the Federal Reserve. (b) Loans to depository institutions 0.09 (c) Federal Reserve float. (d) Other Federal Reserve assets. Total Reserve Bank credit 0. () Gold stock.00 () SDR certificates 0. () US Treasury currency and coin outstanding.99 Total supply of base money other than Reserve Bank credit. () Total supply of base money.9 * $ billions, not seasonally adjusted. Components may not add to totals due to rounding. Source: Board of Governors of the Federal Reserve System. Factors Using Base Money: Current Measure of the Monetary Base () The Monetary Base: Current Measure (a) Currency and coin in circulation 9. (b) Reserve balances of depository institutions at Federal Reserve Banks 0.0 Total monetary base 0.0 () Uses of base money other than as the monetary base (a) Treasury cash holdings 0. (b) Deposits of other than domestic financial institutions at Federal Reserve Banks.9 (c) Other Federal Reserve liabilities and capital. (d) Deposits, other than reserve balances, of domestic financial institutions at Federal Reserve Banks, including contractual amount of required clearing balances. Total other factors using base money.9 Factors Using Base Money: Revised Measure of the Monetary Base () The Monetary Base: Revised Measure (a) Currency and coin in circulation 9. (b) Deposits of financial institutions at Federal Reserve Banks (revised measure). Total monetary base.0 (9) Uses other than as the monetary base (a) Treasury cash 0. (b) Deposits of other than domestic financial institutions at Federal Reserve Banks.9 (c) Other Federal Reserve liabilities and capital. Total other factors using base money (revised measure) 0.0 b). Reserve balances, measured by subtracting the aggregate amount of depository institutions required clearing balance contracts from their aggregate Federal Reserve deposits, is an accounting concept intended to measure the aggregate amount of high-powered money available to support deposit expansion. Uses of highpowered money other than as the monetary base, including their use to satisfy required clearing balance contracts, were about $ billion in December 99 (line ). The new measure of the monetary base (line ) equals the sum of currency in circulation (line a) plus all Federal Reserve deposits held by domestic depository institutions (line b). The new measure recognizes the similarity between the Federal Reserve deposits classified as reserves balances (line b) and those classified as held to satisfy required clearing balance contracts (line d). Both categories of deposits are used by depository institutions to settle interbank payments, and both are available to satisfy legal reserve requirements (albeit perhaps at the cost of failing to satisfy a required clearing balance contract). Including in the monetary base those Federal Reserve deposits putatively held to satisfy required clearing balance contracts increases the amount of Federal Reserve deposits in the base by about one-fourth. Our new measure of the monetary base is suggested by the definition of Balbach and Burger (9):... (the monetary base) can therefore be identified in any monetary system

3 by ascertaining and summing the following:. those assets which the consolidated banking sector uses to settle interbank debt; and. those items, aside from bank liabili ties, which are used as money; and by the definition of the Advisory Commission on Monetary Statistics (9, p. ): With respect to monetary aggregates, one basis for defining such a total is to regard money as corresponding to assets that are generally used to discharge obligations and that are not the explicit liability of nongovernmental entities in the society. Traditionally, such assets have corresponded to specie. In the United States today they correspond primarily to the non-interest-bearing fiat issues of the ultimate monetary authority. The terms high-powered money and monetary base have been used to refer to this total. We shall refer to it as the base. For the United States today the base includes all currency outside the Federal Reserve and the Treasury plus all bank deposits at Federal Reserve Banks. Although broader than the old measure it replaces, the new measure of the monetary base excludes an important asset that these definitions suggest should be included: the amount of intraday credit, in the form of Federal Reserve deposits, used by banks for interbank payments. During 99, such intraday deposits averaged approximately $0 billion, or nearly twice the close-of-business-day amount of Federal Reserve deposits included in the monetary base (see Richards, 99, p. 0). The major barrier to inclusion of intraday deposits is the lack of timely published data: close-of-business deposit levels are published weekly on the Board of Governors H.. statistical release, while intraday credit is not published in any release. The need to revise the measure of the monetary base arises from changes in U.S. financial markets since the Monetary Control Act of 90. The Act significantly changed the demand for Federal Reserve deposits. rior to the Act, almost all deposits at Federal Reserve Banks were held by member banks of the Federal Reserve System. Banks used these balances both to satisfy reserve requirements and to make payments on behalf of customers. For most member banks, the latter came free : the amount of reserves that they were required to hold against deposits was more than sufficient to satisfy any demands arising from interbank payments (perhaps with some intraday Federal Reserve overdraft credit). Nonmember banks and thrifts, lacking access to the Federal Reserve s books for final settlement of payments, made interbank payments and settled checks through correspondent accounts at member banks. The Monetary Control Act made nonmember institutions subject to Federal Reserve System reserve requirements and, at the same time, gave them direct access to the payments system through deposits at the Federal Reserve Banks (see Gilbert and Summers, 99). Because the new reserve requirements were phased in for these institutions over an eight-year period, many initially found their vault cash more than sufficient to satisfy the requirements. Holding only small amounts of Federal Reserve deposits, some institutions found that overdrafts on Federal Reserve accounts became a problem (see Federal Reserve Bulletin, March 9, pp. -9 and December 9, p. ). As a result, during the early 90s the Federal Reserve required some depository institutions that used Federal Reserve payments services to maintain so-called required clearing balances, or levels of Federal Reserve deposits above and beyond the amounts necessary to satisfy the institutions statutory reserve requirements. To offset the cost of holding these balances and make the requirement more palatable, the Federal Reserve paid the institutions, at (approximately) the federal funds rate, earnings credits that could be used only The revised measure of the base, like previous measures, excludes Federal Reserve deposits held by the U.S. Treasury and by foreign central banks, included in lines b and 9b of Table. These deposits are not used to make interbank payments nor to discharge debts of nongovernmental units; see Advisory Committee on Monetary Statistics (9). Nonmember banks held small amounts of Federal Reserve deposits before 90, apparently used for clearing house payments. The measure of the monetary base proposed by Brunner (9) excluded these deposits. The measures constructed by Cagan (9) and Friedman and Schwartz (9, appendix A) include (estimates of) these deposits.

4 Contrary to the terminology in the quotation, required clearing balances are not (and never have been) included in published Federal Reserve data on reserve balances. There is one exception to this statement. A nonmember depository institution may have a separate clearing balance deposit account at a Federal Reserve Bank if it satisfies its required reserves via a passthrough contract with another eligible depository institution. See Feinman (99) and Hilton, Cohen and Koonmen (99). to defray charges for Federal Reserve priced services such as check clearing and wire transfers. A clear statement of the rationale for the exclusion of required clearing balances from the current measure of the monetary base is provided by Gilbert (9), p. n: Depository institutions maintain clearing balances at Federal Reserve Banks as a means of payment for the fees Federal Reserve Banks now charge for services. Depository institutions receive implicit interest on their clearing balances at the federal funds rate, which may be used to pay the fees on services. Required clearing balances are subtracted in computing the [monetary] source base because clearing balances are part of total reserve balances held by depository institutions at Federal Reserve Banks, but are not related to the levels of deposit liabilities. erhaps reasonable at the time, the required clearing balance contract has evolved into a flexible, voluntary tool of depository institution cash management. Although the contract obliges a depository institution to maintain a larger Federal Reserve deposit than is necessary to satisfy its required reserves, the deposit is neither a distinct type nor separate category of deposit: all of the funds are available to settle interbank payments and may be converted to vault cash if necessary. During the mid-90s, and especially following the February 9 shift to contemporaneous reserve accounting, an increasing number of institutions realized that they could simplify their reserve management by voluntarily agreeing to maintain a required clearing balance. Maintaining a required clearing balance changes the expected cost to the depository of satisfying its statutory reserve requirements because the additional Federal Reserve deposits provide an inexpensive cushion against costly shortfalls relative to statutory reserve requirements. Deficiencies relative to the contracted clearing balance impose little cost on the institution, while permitting it to use all its Federal Reserve deposits to satisfy its statutory requirements. At the same time, the Federal Reserve deposits used to satisfy the clearing balance contract accumulate earnings credits at about the federal funds rate. The Federal Reserve deposits held to satisfy a required clearing balance contract act as a buffer stock relative to the deposits needed to satisfy statutory reserve requirements because, under Federal Reserve accounting rules, balances in a depository s Federal Reserve account are applied first to satisfy its statutory required reserves and only thereafter to satisfy the clearing balance requirement. Hence, when an institution s Federal Reserve deposit balance falls below its expectation, the shortage is recorded in the Federal Reserve s accounting system as a deficiency on a clearing balance requirement rather than as a deficiency on a statutory reserve requirement (provided the sum of vault cash and Federal Reserve deposits exceeds the institution s required reserves). No penalties are imposed for small deficiencies on voluntary clearing balance contracts, and larger shortfalls are penalized at only a or percent annual interest rate (see Stevens, 99). Deficiencies relative to required reserves are subject to significant penalties and administrative counseling, while comparable deficiencies relative to a clearing requirement are subject to minimal penalties. An institution that sometimes has been forced to borrow at either the discount window or a penalty federal funds rate to cover reserve deficiencies may find the required clearing balance account comforting. By 9, about 00 institutions had clearing balance contracts, totaling approximately $. billion (Figure ). These numbers were about the same in the third quarter of 990, before the December 990 reduction in reserve requirements on nonpersonal time deposits and certain other liabilities. Two years later, during the third quarter of 99, the amount of contracted required clearing balances had

5 nearly tripled to approximately $. billion while the number of institutions had increased to about 00. In summary, proper measures of the monetary base should include deposits held at Federal Reserve Banks to satisfy required clearing balance contracts, for several reasons: First, the size of a contract, and hence the amount of additional Federal Reserve deposits that must be held to satisfy the contract, is determined by a depository institution s asset and liability management strategy, not by any regulation. An institution may change the size of its clearing balance commitment when it desires, appropriate to its business needs. 9 Required clearing balance contracts are voluntary commitments. Second, the Federal Reserve deposits held to satisfy a clearing balance contract are available to settle interbank payments in the same way as other Federal Reserve deposits. These deposits are maintained in the same Federal Reserve account that contains deposits used to satisfy statutory reserve requirements. Finally, the Federal Reserve deposits used to satisfy required clearing balance contracts are supplied by the Federal Reserve, through actions such as open market operations, in the same way as other high-powered money. They are not a distinct type of funds. Including the amount of required clearing balance contracts in the monetary base is not without objection. Some depository institutions seem to adjust the size of their contract inversely to changes in the federal funds rate, seeking perhaps to generate only enough earnings credits to pay for their use of the Federal Reserve s priced services. For these institutions, the demand for Federal Reserve deposits may be highly interest-elastic and largely unrelated to either liquidity management or lending decisions. If so, argue some analysts, required clearing balances should be excluded from the monetary base. Figure Required Clearing Balance Contract Amounts Billions of Dollars February 99, Increase in federal funds rate target April 99, Reduction in reserve requirements 0 Jan 0 Jan Jan 90 Jan 9 Jan 00 Relatively simple macroeconomic analysis shows that this argument has no implications for definition or measurement of the adjusted monetary base. In previous articles, we have explored the dependence of most money multiplier components, such as k and e, on economic variables such as interest rates and income (Anderson and Rasche, 9; Anderson, Johannes and Rasche, 9). Although it seems likely that including required clearing balances in the monetary base will increase the interest elasticity of the excess reserve ratio, e, this increase has no implications for the importance of the adjusted base as a policy indicator in models where changes in the adjusted monetary base are transmitted to the economy solely through changes in a monetary aggregate, M. In these models, the role of the adjusted monetary base as an indicator of the stance of monetary policy is independent of the size of the elasticity of multiplier components such as k (the nonbank public s desired ratio of currency to checkable deposits) and e (depository institutions desired ratio of excess reserves to checkable deposits) with respect to April 99, Nationwide spread of OCD sweep programs begins December 990, Reduction in reserve requirements The actual amount of Federal Reserve deposits used to satisfy depositories clearing balance contracts is not available. These data are the nominal contracted amounts. 9 However, Federal Reserve operating rules generally discourage changes more frequently than once a month, or approximately every third or fourth maintenance period.

6 0 In this article, we make an additional change to the Burger and Rasche methodology. They proposed that a single RAM adjustment be used in creating the adjusted monetary base. We adopt the proposal of Tatom (90), who observed that the RAM adjustment was appropriate only for changes in reserve-requirement ratios within a given overall structure of requirements. variables such income and interest rates. For further discussion, see Anderson and Rasche (99b). Comparison of U.S. and foreign payments systems reinforces our decision to include the aggregate amount of required clearing balance contracts in the monetary base. In some countries, depository institutions need to settle interbank payments in central bank deposits has been cited as a justification for effective, binding statutory reserve requirements (Deutsche Bundesbank, 99, pp. 0-0). In countries without statutory reserve requirements, all central bank deposits held by depository institutions are clearing balances; yet, such deposits play an important role in the central bank s monetary policy (see Bank of Canada, 9, 99, 99; Bank for International Settlements, 99). ADJUSTING THE MONETARY BASE FOR CHANGES IN RESERVE REQUIREMENTS The adjusted monetary base combines in a single index three Federal Reserve actions that affect the supply of the monetary base open market operations, discount window lending, and unsterilized foreign exchange market intervention with changes in statutory reserve requirements that affect depository institutions demand for the monetary base. Hence, measuring the adjusted monetary base requires a mechanism that can translate changes in the demand for base money due to changes in statutory reserve requirements into equivalent changes in the supply of base money due to open market operations or similar actions. The reserve adjustment magnitude, or RAM, provides such a mechanism by measuring the amount by which the aggregate quantity of base money demanded by depository institutions during any given period has been affected by changes in reserve requirements, relative to a selected base period. Combining the effects of changes in statutory reserve requirements with those from open market operations and similar instruments depends, implicitly or explicitly, on a model of depository institutions demand for base money. Absent a fully worked out model of bank liquidity management and reserve demand, we use statistical tests to identify the characteristics of depositories that likely have, and have not, responded to changes in reserve requirements since 90. Only the former set of institutions is included in our new RAM adjustment. The original St. Louis adjusted monetary base published by Andersen and Jordan (9) included an adjustment for reserves released by changes in reserve requirements. The adjustment, constructed as suggested by Brunner (9), added to the monetary base at each date the cumulative dollar amount by which past changes in reserve requirements had changed the level of required reserves. Although each change in reserve requirements was viewed as absorbing or liberating a certain dollar amount of required reserves, these amounts depended only on the amount of reservable deposits on the date of the reduction: They did not vary in later periods with changes in the levels of reservable deposits. In 9, Burger and Rasche (9) showed that Brunner s adjustment for the effects of reserve-requirement ratio changes was inadequate because it did not consider the amount by which past changes in reserve-requirement ratios affected banks current required reserves. They showed that a suitable adjustment must vary with current deposit levels if it is to remove the total effect of the change in reserve-requirement ratios from the monetary base multiplier (and no more). They proposed that the adjusted monetary base be measured as the sum of the monetary (source) base and a time-varying reserve adjustment magnitude (RAM), a methodology that has generally been maintained in subsequent revisions of the St. Louis adjusted monetary base. 0 Substantial changes in the structure of reserve requirements since 90 suggest a reexamination of the Burger and Rasche

7 methodology. We formalize their analysis by considering a model with two classes of institutions. Those in the first class resemble the member commercial banks considered by Burger and Rasche: Their required reserves exceed their vault cash, and they must hold deposits at Federal Reserve Banks to satisfy the balance of their statutory requirements. As a result, statutory reserve requirements play an important role in determining their demand for base money. Institutions in the second class find legal reserve requirements much less influential in their portfolio allocation decisions: Their level of required reserves is less than their vault cash, and they need not hold any deposits at Federal Reserve Banks to satisfy statutory requirements. The demand by these institutions for deposits at Federal Reserve Banks depends largely on their need to make interbank payments in immediately available funds on the books of the Federal Reserve Banks, and perhaps on Federal Reserve restrictions regarding daylight overdrafts. Monetary Base Multipliers before 90 We begin with a model that reflects the institutional environment before the Monetary Control Act of 90. Since our purpose is to illustrate the dependence of the RAM adjustment on the distribution of deposits among different classes of depository institutions, we separate member and nonmember banks more explicitly than have previous authors. We assume () a central bank that issues two liabilities, currency, Cu, and reserve balances (that is, deposits at the central bank), RB, and () two types of depository institutions, indexed by superscripts M and N (corresponding to member banks, and to non-member banks and thrifts, respectively), that issue demand D = D M D N and time T = T M T N deposits. The two types of depositories are dissimilar in four characteristics: Type M institutions are subject to central bank reserve requirements against deposits that may be satisfied by holding either vault cash or deposits at the central bank. Government deposits are only at type M institutions. Type N institutions hold deposits at type M institutions but not vice versa. Type N institutions are not permitted to hold deposits at the central bank. They are similar in two other ways: Both types of institutions hold vault cash to satisfy reserve requirements and/or to convert deposits into currency on demand. Both types of institutions issue deposits that the nonbank public regards as perfect substitutes. We assume that transactions among banks, the government, and the nonbank public are settled in terms of currency, Cu, demand deposits held by the government G at type M depositories, D M, demand deposits held by the nonbank public at type M and N depositories, D M and D N, respectively, and demand deposits held by N type N at type M depositories, D M. (Throughout, superscripts refer to the owner of the deposit and subscripts to the issuer of the deposit.) Define D = D + D M and note that N and D = D + D + D, M M M G M N D = D + D D D M N M G M N The Federal Reserve imposes reserve requirements against demand D M and time T M deposits at rates r D and r T, respectively, such that the required reserves of a type M institution are RR = r D D M r T T M. The monetary base multiplier in this model is easily derived. Suppressing time subscripts, the monetary base is by definition MB = RB Cu = r D D M r T T M k D VC N (VC M RB r D D M r T T M ) = (r D d M r T t M k v N e M )D, where (r D D M r T T M ) are the required reserves of type M institutions,. See for example Hancock and Wilcox (99). Burger (9) provides a similar analysis without as explicit a separation of different classes of institutions. Historically, some nonmember banks and thrifts faced stateimposed reserve requirements that had to be satisfied with holdings of vault cash, deposits in other banks, U.S Treasury bills or certain other liquid securities. See Gilbert (9), Gambs and Rasche (9), and Gilbert and Lovati (9). 9

8 See Table.0 in the Federal Reserve Bulletin or the Board s weekly statistical release Aggregate Reserves of Depository Institutions and the Monetary Base. (H.) k D is currency held by the nonbank public, VC M and VC N are vault cash held by type M and N institutions, respectively, RB are the deposits held by type M institutions at the central bank, d M DM TM VCN =, t v M =, N =, D D D D M T M VC and M + RB r D r T e. M = D The term (VC M RB r D D M r T T M ) equals the amount of high-powered money, vault cash plus reserve balances, held by type M institutions above and beyond their required reserves. For clarity, it may be useful to relate these reserve constructs in our model to those currently published. The Federal Reserve Board s reserve measures differ from those of the Federal Reserve Bank of St. Louis by excluding surplus vault cash from the definition of excess reserves. For an individual depository institution i, if VC i,m (r D D i,m r T T i,m ), then the difference (VC i,m r D D i,m r T T i,m ) is referred to as surplus vault cash. If VC i,m (r D D i,m r T T i,m ), then surplus vault cash is zero. If VC i,m (r D D i,m r T T i,m ) and RB i,m 0, then RB i,m RCB i,m is referred to as excess reserves, where RB i,m represents the total reserve balances held by depository institution i at the Federal Reserve and RCB i,m is the amount of its required clearing balance contract (if any). Note that RCB i,m may be zero, and RB i,m RCB i,m may be negative. If RB i,m RCB i,m = 0, then excess reserves equal zero even though surplus vault cash is greater than zero. If VC i,m (r D D i,m r T T i,m ), then RB i,m RCB i,m (r D D i,m r T T i,m VC i,m ) is excess reserves. Measures of aggregate total and excess reserves published by the Board of Governors of the Federal Reserve System omit surplus vault cash and an amount of Federal Reserve deposits equal to depository institutions required clearing balance contracts. The old reserve measures published by the Federal Reserve Bank of St. Louis through September 99 (discussed in the previous section of this paper) included surplus vault cash but omitted required clearing balance contracts. The monetary base multiplier for M is straightforward: M = Cu + D = + k D ( + k) = r d + r t + k + v + e and for M, D T M M N M D T = ( M M M N ) m r, r, k, e, t, t, d, v MB, ( ) ( ) M = Cu + D + T = + k + t D ( + k + t) = r d + r t + k + v + e D T M M N M D T = ( M M M N ) m r, r, k, e, t, t, d, v MB, ( ) + = ( ) M M TM TN where t =. D D The reserve adjustment to the monetary base, RAM, maps the effects of changes in reserve-requirement ratios into equivalent changes in the monetary base. The effect of this mapping is to define new adjustedmonetary-base multipliers for the monetary aggregates M and M that are invariant to changes in the reserve-requirement ratios r D and r T, denoted as m b (r D,r T,k,e M,t,t M,d M,v N ) and m b (r D,r T,k,e M,t,t M,d M,v N ), respectively. At the same time, the adjustment should not change the response of these multipliers to arguments other than the reserverequirement ratios r D and r T, when compared to the responses of m b (r D,r T,k,e M,t,t M,d M,v N ) and m b (r D,r T,k,e M,t,t M,d M,v N ). Letting the adjusted monetary base be defined as AMB = MB + RAM, we have: M = m b (MB RAM) = m b AMB where ( + k) mb =, D T r0 d M + r0 t M + k + v N + e M MB MB and 0

9 r and r T 0 D 0 are the reserve requirement ratios on transaction and time deposits in a chosen base period, respectively. The reserve adjustment magnitude, maps the change in required reserves due to any change in reserve requirement ratios since the specified base period into an equivalent change in the monetary base. Similarly, for M we have M = m b AMB = m b (MB RAM). Noting that then ( ) + ( ) D RAM r rt D T = dm r rt T t 0 0 M D [ + k + t] D = mb[ rt ] D dm rt T tm k vn em D + D m ( r0 r ) d + ( r0 r b t ) t D, T T m t T m ( + k + t) mb = D T r0 d m + r0 t m + k + v N + e m which is invariant to changes in the legal required reserve ratios r D and r T. The above analysis may be extended to the case where type M institutions (those subject to central bank reserve requirements) issue i = (,...,I) classes of transaction deposits and j = (,...,J) classes of time deposits, each with possibly different reserve requirement ratios. At type M institutions, let DMi TMj δ Mi = and τ Mj = D D denote the ratios of the nonbank public s holdings of demand and time deposits in the i th and j th reserve classifications, respectively, to their total holdings of demand deposits, D. Then aggregate required reserves are I i= J rmi D T δ + r τ D Mi Mj Mj, j= and the monetary base multiplier is,, m Note the presence of base-period reserve-requirement ratios for each class of D T deposit, r Mi0 and r Mj0, in the denominator. The corresponding reserve adjustment magnitude is I D RAM = ( rmi rmi ) D Mi + 0 δ J rmj T rmj T 0 τ Mj D. j= Finally, as a caveat and extension to earlier remarks, note that the RAM adjustment does not make all money and credit multipliers invariant to changes in statutory reserve-requirement ratios. Consider the monetary-base multiplier for bank credit (BC), or m BC, defined by Brunner and Meltzer (9) as BC = m BC MB. In our notation, [see Brunner and Meltzer (9), equation A., p. ]. Let the adjusted-monetary-base multiplier for bank credit be defined as BC = m BCb AMB = m BCb [MB RAM]. Then: ( + t) ( r t d r t e v ) D m t T m m N D so b + k = I J D T rmi0 Mi + rmj0 + k + v + e δ τ i= j= m which is not invariant to change in legal required reserve ratios r D and r T. Thus, in models in which intermediated (bank) credit provides a channel of monetary policy independent of that provided by monetary aggregates, the adjusted monetary base defined above is not an adem BC BCb i= ( ) Mj N M ( t D m t T m m N ) ( ) t r d r t e v = r d + r t + k + e + v t D m t T m m N [ ] + BCb t D m + t T m + m + N D ( 0 ) + ( 0 BCb t ) D T m t T m m r d r t e v D m r r d r r t D ( t D m t T m m N ) ( ) t r d r t e v = r d + r t + k + e + v D T 0 m 0 m m N =,., Recall that only type M institutions are subject to statutory reserve requirements in this model.

10 In 9, required reserve ratios at member banks ranged from a minimum of percent on the first two million of net demand deposits to. percent on net demand deposits in excess of 00 million dollars. The required reserve ratio on savings deposits was percent and the reserve requirements on time deposits maturing in less than 0 days were percent on the first $ million and percent on time deposits in excess of $ million. (Federal Reserve Bulletin, December, 9, p. A9) In 99, the reserve requirement ratio on the first $. million of net transaction deposits was zero (the reserve exemption amount), and only percent on the next $ million (the low reserve tranche). The cutoff for the low reserve tranche is changed annually. Reserve requirements were increased from zero on all nonmember depository institutions. The full imposition of reserve requirements on these institutions was phased in over the period between 9 and 9. quate indicator variable for the stance of monetary policy. Adjusting for Reserve Requirement Changes with Economically Nonbound Institutions For periods prior to late 90, depository institutions are easily separated into two groups based on their holdings of base money: Member banks held vault cash, were subject to Federal Reserve System reserve requirements, and generally held deposits at Federal Reserve Banks; nonmember banks and thrifts held vault cash and were not eligible to hold deposits at Federal Reserve Banks. Studies of the adjusted monetary base prior to 90 generally assumed that member banks changed their holdings of base money about dollar-for-dollar following changes in their required reserves due to changes in reserve-requirement ratios. During that period, member banks held few excess reserves, and most banks likely faced reserve-requirement ratios sufficiently high to constrain their portfolio allocation decisions. The use of Federal Reserve deposits to settle interbank payments was little discussed. The general assumption among economists and banking analysts seemed to be that either banks deposits at Federal Reserve Banks were more than adequate to absorb debits and originate payments, or that the Federal Reserve would supply adequate intraday credit. Banks also had very limited ability to alter their demand for base money by inducing customers to shift funds from transaction to nontransaction deposits. Time deposits, with the exception of large negotiable certificates of deposit, were subject to effective Regulation Q interest rate ceilings. Overall, both banks and their customers likely were sufficiently constrained that other multiplier components (such as the ratio of time and savings deposits to transaction deposits, or t) were unaffected by changes in legal reserverequirement ratios on deposits. Under this regime, the total amount of base money demanded by depositories equaled the sum of member banks required and excess reserves, plus the vault cash held by other depositories. Because member banks applied essentially all their vault cash to satisfy reserve requirements, and because required clearing balances were approximately zero, excess reserves at member banks equaled the difference between their deposits at Federal Reserve Banks (denoted as RB) and the portion of their required reserves not satisfied by vault cash: ER M = RB M (r D D M r T T M VC M ). (Note that RB denotes both the reserve balances and total Federal Reserve Bank deposits held by member banks; without required clearing balance contracts, these are exactly the same.) Excess reserves for the banking system as a whole equaled the sum of excess reserves at member banks plus vault cash at nonmember banks, VC N. The average aggregate excess reserve ratio was ERM + VCN e = em + vn =. D Today s environment is considerably different. The Monetary Control Act extended reserve requirements to all depository institutions, reduced to zero required reserves on savings and personal time deposits, and significantly reduced other reserve requirements on member banks. During December 990 and January 99, reserve-requirement ratios on nonpersonal time deposits and Eurodollar liabilities were reduced to zero for all depository institutions. In April 99, reserve-requirement ratios on transaction deposits were reduced to 0 percent from percent. Depository institutions also gained greater freedom to adjust their mix of reservable and nonreservable deposits during the 90s, following the end of Regulation Q ceilings on deposit offering rates. Following implementation of the Monetary Control Act, many depository institutions found that their vault cash, although largely held for retail business reasons, also satisfied their reserve requirements. In the Federal Reserve System, depository institutions that fully satisfy

11 their required reserves with vault cash are known as nonbound institutions; other institutions are known as bound institutions. In this article, we refer to these institutions as L-Nonbound and L-Bound, respectively. Table shows the percentage distribution of L-Bound and L-Nonbound depository institutions among depositories reporting data to the Federal Reserve for selected years from 9-9. (The rows labeled E-Bound and E-Nonbound are explained later.) art A of the table includes only institutions that reported data weekly, while art B includes institutions that reported quarterly and annually. 9 In mid-9, after the initial phase-in of the Monetary Control Act, about 0 percent of the total deposits reported by weekly-reporting institutions was at L-Nonbound institutions; for all reporting institutions, shown in art B, about percent of deposits was at L-Nonbound institutions. By mid-99, these proportions had fallen to approximately percent (in art A) and percent (in art B). The reduction in reserverequirement ratios increased the proportion of total deposits at L-Nonbound weekly reporting institutions to about percent in 99. We regard L-Nonbound institutions as facing no effective reserve requirement related constraint because they seem unlikely to change the asset mix of their portfolios following a change in statutory reserve requirements. L-Nonbound institutions satisfy their required reserves with vault cash, and we assume that their holdings of vault cash are determined almost entirely by business needs, rather than by statutory reserve requirements. As a result, these institutions seem unlikely to change their portfolio mix of assets in response to a change in reserve-requirement ratios. Vault cash held by L-Nonbound depository institutions in excess of their required reserves is known as surplus vault cash. Surplus vault cash is surplus only in the sense that some part of the bank s vault cash is not used to satisfy statutory reserve requirements. No statutory requirement determines a depository s vault cash; these amounts are voluntarily chosen by the institutions managers. As such, they presumably reflect anticipated business of the institution, and hence are not surplus in the economic sense of indicating a portfolio disequilibrium. Surplus vault cash is included in both the old and new St. Louis measures of the adjusted monetary base, and in the Board of Governors measure of the monetary base, not adjusted for reserve requirement changes and not seasonally adjusted. It is excluded, however, from the Board of Governors measure of the monetary base, adjusted for changes in reserve requirements. Historical data on surplus vault cash are shown in Figure (see page ). Before 99, vault cash could not be used to satisfy reserve requirements, so all vault cash was surplus. Surplus vault cash decreased sharply during 99-0 when Federal Reserve member banks were gradually allowed to apply vault cash toward satisfying required reserves. (The fraction of vault cash eligible to satisfy required reserves increased linearly at the rate of one-twelfth per month, reaching 00 percent of vault cash in December 90.) From 9 to 9, surplus vault cash equaled the vault cash held by nonmember banks and thrift institutions, since member banks applied virtually all their vault cash to satisfy reserve requirements. Surplus vault cash grew rapidly during the 90s as the fraction of banks that were members of the Federal Reserve System declined. Although the Monetary Control Act extended reserve requirements to all depository institutions, the requirements were phased in during During these years, surplus vault cash generally decreased. During the later 90s, surplus vault cash remained relatively constant but exhibited substantial seasonal variation. Although the vault cash holdings of L-Bound institutions are less than their required reserves, some of these institutions also might not be constrained by legal reserve requirements. For some of these institutions, especially smaller ones, statutory reserve requirements might not be an important factor in their portfolio 9 For weekly-reporting institutions, the data are the first reserve maintenance period that begins and ends in July of the specified year. June data are used for quarterly and annual reporters.

12 Table Statistics on Legally and Economically Bound and Nonbound Depository Institutions, Selected Years A. Weekly Reporting Depository Institutions (Federal Reserve FR900 report) Distribution of Reporting Depository Institutions, by reserve status (percent of reporting institutions) L-Bound L-Nonbound E-Bound E-Nonbound Distribution of Total Deposits, by reserve status (percent of total deposits of weekly reporters) L-Bound L-Nonbound E-Bound E-Nonbound Distribution of Net Transactions Deposits, by reserve status (percent of aggregate net transactions deposits of weekly reporters) L-Bound L-Nonbound E-Bound E-Nonbound Distribution of Required Reserves, by reserve status (percent of aggregate required reserves of weekly reporters) L-Bound L-Nonbound E-Bound E-Nonbound B. Statistics on the Sum of Weekly, Quarterly and Annual Reporting Depository Institutions Distribution of Reporting Depository Institutions, by reserve category (percent of reporting institutions) L-Bound L-Nonbound E-Bound E-Nonbound Distribution of Total Deposits, by reserve category (percent of reported total deposits) L-Bound L-Nonbound E-Bound E-Nonbound Notation: L-Bound denotes legally bound, L-Nonbound denotes legally nonbound (applied vault cash exceeds required reserves), E-Bound denotes economically bound (as defined in this article), E-Nonbound denotes economically nonbound. All quarterly and annual reporting institutions are considered as both legally and economically nonbound in the construction of this table. Source: tabulations by the authors from unpublished Federal Reserve data.

13 decisions. In this article, we denote such economically-nonbound institutions as E- Nonbound, and other institutions for which reserve requirements are binding in the traditional sense of constraining their asset portfolio choices as E-Bound. How might the portfolio reactions of E-Bound and E-Nonbound institutions to changes in reserve-requirement ratios differ? The depository institutions ordinary business somewhat restricts their responses. Generally, an institution must maintain adequate stocks of vault cash to convert customer deposits into currency on request, and of Federal Reserve Bank deposits to originate and absorb interbank payments. However, both constraints are somewhat flexible. There is an intraday market in vault cash, at least within larger cities, suggesting that a bank might ask a customer who is seeking a large amount of cash to wait until later in the day, when adequate currency can be obtained from the Federal Reserve or from a correspondent. Some banks require customers who are planning to withdraw a significant amount of currency to provide at least one business day s notice. It also is not uncommon for ATM machines to run out of currency. For Federal Reserve Bank deposits, there is a national secondary market, the federal funds market. For interbank payments, the Federal Reserve may delay an interbank payment if it exceeds applicable daylight or overnight overdraft limitations. Because a failure to convert a deposit into currency or to make a requested interbank payment may damage a customer relationship, a depository cannot be indifferent to its mix of vault cash and Federal Reserve Bank deposits. The economic distinction between E- Bound and E-Nonbound institutions is illustrated by the response of their excessreserve ratio to changes in reserve-requirement ratios. For E-Bound institutions, changes in reserve-requirement ratios, within the range where the requirement remains a constraint on the institutions portfolios, will induce the institutions to match changes in required reserves with Figure Surplus Vault Cash Billions of Dollars hase-in of applied vault cash at member banks November 90, Monetary Control Act 0 Jan Jan 0 Jan 0 Jan 0 Jan 90 Jan 00 dollar-for-dollar changes in base money. As a result, excess reserves (base money held in excess of statutory requirements) will be approximately unchanged. If all depository institutions are E-Bound, then a change in reserve-requirement ratios will leave the aggregate excess reserve ratio, e, almost unaffected. The best-known historical example of this type of portfolio adjustment is member banks reaction to the 9- increase in reserve-requirement ratios. Contrary to expectations of Federal Reserve officials, member banks excess reserve ratios did not fall sharply following the increases. 0 Surplus deposits at Federal Reserve Banks, excess in the sense that they were not applied to satisfy statutory required reserves, were in fact an optimal portfolio choice by member banks; the deposits were not excess in any economic sense. The reserve-requirement ratios of 9 were effective constraints on the banking system, with almost all member banks E-Bound. In contrast, consider the portfolio response of E-Nonbound depository institutions to a change in reserve-requirement ratios that leaves the institutions E- Nonbound after the change. The institu- 0 See Friedman and Schwartz (9), pp. -, for a discussion of the changes in reserve requirements and documentation that the Fed anticipated that the increases in reserve-requirement ratios would substantially reduce the excess reserves of the banking system. Note that only deposits at Federal Reserve Banks were eligible to satisfy reserve requirements (vault cash didn t become eligible until 99).

14 See Richards (99) or Hancock and Wilcox (99). tions business needs, not legal reserve ratios, are the primary determinant of their base money holdings. The excess reserves of E-Nonbound institutions will vary approximately dollar-for-dollar but in the opposite direction to the change in required reserves, leaving total base money holdings largely unaffected. The behaviors of surplus vault cash and required clearing balance contracts after the and 99 changes in reserve requirement ratios suggest that a substantial proportion of depository institutions are E-Nonbound. Surplus vault cash, shown in Figure, increased sharply in 99 after reserve-requirement ratios were reduced to zero from percent on nonpersonal time deposits and Eurodollar liabilities. This increase suggests that at least some depository institutions with surplus vault cash were E-Nonbound during 990. More dramatic perhaps was the sharp increase in required clearing balance contracts, shown in Figure. Although almost all E-Bound institutions reduced their holdings of Federal Reserve Bank deposits after the reduction in reserve-requirement ratios, some found that attempts to match the reduction in their required reserves with a dollar-for-dollar decrease in their Federal Reserve deposits caused an unacceptable increase in the probability that they might experience either an overnight overdraft or exceed their regulatory cap on daylight overdrafts. This increase also was likely due, at least in part, to depository institutions recognition that Federal Reserve Bank deposits no longer needed to satisfy statutory reserve requirements could be used to satisfy required clearing balance contracts. Note that the 99 surge in required clearing balance contracts occurred after several years of stability in the amount of such balances. The aggregate data on required clearing balance contracts also are consistent, at least in part, with the alternative hypothesis that some part of required clearing balances is held primarily to defray the cost of Federal Reserve priced services. Clearing balances surged during 99 and 99 as growth of the monetary base accelerated and the federal funds rate fell, and they decreased sharply during 99 as growth of the base slowed and the federal funds rate rose. Although some institutions likely adjust the size of their clearing balance contracts inversely with respect to changes in the federal funds rate, the changes in 99 seem too large to be primarily a reaction to a lower federal funds rate. If E-Nonbound institutions represent a significant share of the monetary base held by depository institutions, it is important to separate them from E-Bound institutions when measuring RAM. To make the analysis more precise, consider an economy with two distinct groups of depository institutions, both subject to Federal Reserve System reserve requirements. Define economic excess reserves as ER i = RB i (r D D i r T T i VC i ),i = (EB,EN), where RB denotes total Federal Reserve Bank deposits held by all depository institutions (with no deduction for the amount of required clearing balance contracts), and let the subscripts EB and EN denote groups of E-Bound and E-Nonbound institutions, respectively. E-Bound institutions are assumed to change the amount of base money they demand (relative to reservable deposits) approximately dollar-for-dollar following a change in statutory required reserve ratios. For this group, changes in reserve requirement ratios leave their excess reserve ratio, EREB eeb =, D approximately unchanged. E-Nonbound institutions do not change their holdings of base money (relative to reservable deposits) following a change in reserverequirement ratios. Their excess reserve ratio, e EN ER = D EN,